Furthermore, for the class of local commuting projector codes in \(D\)  dimensions
(a class that generalizes stabilizer codes, but does not contain general subsystem
codes), Bravyi, Poulin, and Terhal [1]} have shown the inequality
\(k d^{2/(D-1)} \le O(n)\) . It is open whether a similar upper bound holds for subsystem codes,
but a corollary of our main results is that there are spatially local subsystem codes
for every \(D\ge 2\)  that obey \(k d^{2/(D-1)} \ge \Omega (n)\) .
